Sigma models as Gross-Neveu models

I will show that there is a wide class of integrable sigma models that are exactly and explicitly equivalent to bosonic/fermionic Gross-Neveu models. In full generality these are models with quiver variety phase spaces, but the familiar $CP^n$, Grassmannian or flag manifold sigma models belong to this class as well. This approach leads to a new take on topics such as RG flow (potentially allowing an all-loop calculation), construction of integrable deformations and the inclusion of fermions. In particular, it provides a way of obtaining worldsheet SUSY theories from target space SUSY theories by means of a supersymplectic quotient. Generalizations to Riemann surface worldsheets will also be mentioned.
This is mostly a review talk based on arXiv:2006.14124, 2009.04608, 2101.11638, 2106.15598, 2202.12805 but will include latest developments as well.